Analyses of thermal buckling and secondary instability of post-buckled S-FGM plates with porosities based on a meshfree method

Abstract

The present research deals with thermal buckling and postbuckling of sigmoid functionally graded material (S-FGM) plates with porosities resting on elastic foundation based on the popular third-order shear deformation theory and the well-known von Kármán large deflection assumption. Special attention is paid to scrutinize the secondary instability that occurs during postbuckling regime. In addition, the transitions of deflection shapes of the plates under various boundary conditions between primary and secondary postbuckling paths are investigated. A displacement control strategy and a meshfree radial point interpolation method (RPIM) which employs a radial basis function without any adaptive parameters are utilized synthetically to carry out thermal buckling loads and postbuckling paths of the plates numerically. Numerical comparisons are performed to verify the convergence of the modified RPIM and the accuracy of iteration method in postbuckling path analysis. The influences of functionally graded index, porosity coefficient and parameters of elastic foundation to behaviors of the thermal buckling and especially the secondary instability occurs during postbuckling regime are investigated. It is found that the secondary instability is sensitive to the boundary conditions.